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Item Generation of Smooth Surfaces by Controlling Curvature Variation(Blackwell Science Ltd and the Eurographics Association, 1996) Higashi, Masatake; Tsutamori, Hideo; Hosaka, MamoruTo satisfy a designer s intention for constructing aesthetic shapes such as automotive bodies, we propose a surface generation method. In the surface design process, designers determine shapes according to their great concern for the reflected images of vehicle surroundings, shade lines and highlight lines. Since reflection and shading are affected by changes of surface normal, the curvature variation of the surface, which represents the change of the surface normal, should be smooth and distributed as designers want. The proposed method controls curvature distribution directly by determining a surface shape from an evolute, which is a locus of the curvature center of the generatrix and moves along directrices to form the surface. It first generates evolutes of boundary curves to be generatrices as rational Bezier curves, then interpolates their shapes with the Bezier polygons, and locates the interpolated shape to the corresponding position of the directrices. By applying this method, we have confirmed that a smooth shape is generated from four boundary curves.Item INTERPOLATING CURVE NETWORKS WITH NEW BLENDING PATCHES(Eurographics Association, 1990) Saitoh, Tsuyoshi; Hosaka, MamoruThis paper describes methods of c o n s t r u c t i n g s u r f a c e patches which s a t i s f y independently given boundary conditions on a l l i t s four or t h r e e s i d e s . A patch c o n s i s t s of two p a r t s : one i s a patch s a t i s f y i n g a t l e a s t p o s i t i o n a l condition of the boundary curves, and the other gives n u l l position vectors and independent i t s f i r s t and second d e r i v a t i v e vectors on t h e i r boundaries. The l a t t e r i s used for compensating d e r i v a t i v e vectors t o s a t i s f y given boundary conditions. A network o f curves whose meshes are four or t h r e e s i d e s can be i n t e r p o l a t e d smoothly with patches of t h i s type.Item Robust Computation of Intersection Graph between Two Solids(Blackwell Publishers Ltd and the Eurographics Association, 1997) Nakamura, Hiroyuki; Higashi, Masatake; Hosaka, MamoruWe propose a new robust algorithm for Boolean operations on solid models. The algorithm produces a consistent intersection graph between two input solids whose geometrical data are represented in floating point numbers. In order to prevent numerical calculation errors and inaccuracy of input data from causing inconsistency of the output, we put higher priority on symbolical connectivity of the edge-face intersection points than their numerical nearness. Each edge-face intersection point is symbolically represented using face names, which generate connectivity relations between the intersection points and the intersection line segments. The symbols with the same connectivity are made into clusters. The intersection line segments connected together at their end clusters form the intersection graph of two solids. Inconsistency of the connectivity of the clusters is detected and the intersection graph is corrected automatically. We describe the algorithm in detail for polyhedral solids, discuss extension to curves solids, and show its effectiveness by some examples of Boolean operations for two solids whose faces intersect at a very small angle.Item On Formulation and Display for Visualizing Features and Evaluating Quality of Free-form Surfaces(Eurographics Association, 1990) Higashi, Masatake; Kushimoto, Takuya; Hosaka, MamoruFor evaluating quality of free-form surfaces and visualizing their features, various curves on a surface, which characterize its properties, are defined and their equations are deduced. Newly introduced curves include those of equi-gradient, silhouette, highlight and a locus of points of extremum gradient on contour curves, loci of points of extremum principal curvature on lines of curvature. The objectives of these curves and their uses are described. Other curves such as contour curves, its orthogonal ones, loci of points of zero curvatures, and lines of curvature as well as umbilics are also treated. Displays of these curves are shown.